Simple exercises

In this topic you will see how Boolean algebra, truth tables and logic gates relate in a series of simple exercises.

Example: Employee access control system

In this example we aim to design a logic circuit that determines whether an employee is permitted access to a restricted area of the data centre.

There are three key factors that determine the decision:

• Valid access card ($T$): The employee must present the card to the reader and it must be recognised as valid.
• Recognised fingerprint ($H$): The employee must scan their fingerprint and it must match the registered one.
• Security clearance ($S$): The employee must hold an active security clearance for this area.

The rules for granting access are:

• $R_1$ - The card is valid and the fingerprint is recognised.
• $R_2$ - The security clearance is active and the fingerprint is recognised.
• $R_3$ - The security clearance is not active and the card is valid.

We need to design a circuit with three inputs ($T$, $H$, $S$) and one output ($A$). The output $A$ determines whether access is granted, taking the value 1 for granted access and 0 for denied access.

First, we construct the truth table of the application:

$T$	$H$	$S$	$R_1$	$R_2$	$R_3$	$A$
0	0	0	0	0	1	1
0	0	1	0	0	0	0
0	1	0	0	1	1	1
0	1	1	0	1	0	1
1	0	0	0	0	1	1
1	0	1	0	0	1	1
1	1	0	1	0	1	1
1	1	1	1	1	1	1

Next we express the Boolean function of the operation:

$$A=R_1+R_2+R_3=(TH)+(SH)+(\bar{S}T)$$

Next we draw the digital circuit:

Exercises on Jutge.org: Introduction to Digital Circuit Design

• The Embassy Ball
• Heating-cooling system
• Energy-efficient heating-cooling system
• Robot with light sensors

Remember that to access the exercises and for the Jutge to assess your solutions you must be enrolled in the course. You will find all the instructions here.

Xavier Casas, Francesc Madrid
Lliçons.jutge.org
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